A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.

What is an actuary? An actuary is an expert in statistics who works with businesses, governments, and organizations to help them plan for the future. Actuarial science is the discipline that applies math and statistical methods to assess risk.

Background photo: © Inga Nielsen/iStockphoto.

6-8

DURATION
30

COLLECTION
The Power of Probability

# Lesson 3: Compound Probability

STANDARDS (CCSS AND NCTM)

• Grade 7: Statistics and Probability (CCSS 7.SP.8)
• Grades 6–8: Construct Viable Arguments & Model with Mathematics (CCSS MP3 and 4)
• NCTM: Data Analysis and Probability

OBJECTIVE

• Students will use a tree diagram to derive the formula for compound probability; and
• Students will use the formula for compound probability to calculate the probability of multiple independent events.

MATERIALS

Click for whiteboard-ready printables.

DIRECTIONS

Introduction to Compound Probability

1. Show the coin to the class and ask what is the probability of the coin landing on heads.

2. Recall the work done in Lesson 1 on tree diagrams and ask for a volunteer to explain how all the outcomes for three flips in a row could be depicted.

3. Ask what the probability of a coin landing on heads three times in a row would be. Walk the students through a tree diagram to demonstrate that there is one outcome for three heads in a row while there are seven unfavorable outcomes (HHT, HTT, HTH, TTT, TTH, THT, THH), so the probability is one out of eight or 1/8 or 12.5%.

4. Ask if there is a way to calculate the probability of tossing three heads in a row without setting up the tree diagram. If necessary, point out that the probability of one heads flip is 1/2 or 50% or .5 and, for three heads in a row:
1/2 x 1/2 x 1/2 = 1/8 or
.5 x .5 x .5 = .125 or
50% (.5) x 50% (.5) x 50% (.5) = 12.5% or .125

5. Guided Practice: Individually or in pairs, ask students, using both the formula and a tree diagram, to determine:

• The probability of rain in both Chicago and San Francisco on the same day if the probability of rain is 20% in Chicago and 50% in San Francisco (20% x 50% = 10%)
• The probability of a six-sided die landing on an even number then flipping heads (50% x 50% = 25%)

Ask students to explain their answers to the class.

7. Distribute Worksheet 3. Read the introduction and review the facts with the class. Ask students to complete the worksheet. Review answers as a class. Worksheet Answer Key (PDF). As a bonus activity, have students complete the Bonus Worksheet.

LESSON EXTENSION
Have students use the Online Probability Challenge to practice using probability skills for real-life purposes. This interactive online activity challenges students to use probability to help Rick and Athena plan a summer concert tour. This activity can be used as an in-class lesson activity or an out-of-the classroom extension.

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